Unitarity and microscopic acausality in a nonlocal theory

TL;DR

This paper investigates unitarity and causality in a nonlocal higher-derivative quantum field theory with infinite derivatives, highlighting potential phenomenological signatures and differences from Lee-Wick theories.

Contribution

It introduces a nonlocal higher-derivative framework that maintains unitarity without additional poles, offering new insights into addressing the hierarchy problem.

Findings

Propagators decay faster in the ultraviolet due to entire functions.

Tree-level propagators lack additional unobserved particle poles.

Microscopic acausality may produce observable phenomenological signatures.

Abstract

We consider unitarity and causality in a higher-derivative theory of infinite order, where propagators fall off more quickly in the ultraviolet due to the presence of a transcendental entire function of the momentum. Like Lee-Wick theories, these field theories might provide new avenues for addressing the hierarchy problem; unlike Lee-Wick theories, tree-level propagators do not have additional poles corresponding to unobserved particles with unusual properties. We consider microscopic acausality in these nonlocal theories. The acausal ordering of production and decay vertices for ordinary resonant particles may provide a phenomenologically distinct signature for these models.